名校
1 . 已知四棱锥
,底面ABCD为菱形,
,H为PC上的点,过AH的平面分别交PB,PD于点M,N,且
平面AMHN.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/25/7e759ab8-6677-4d09-8c63-b963dc0752cc.png?resizew=237)
(1)证明;
;
(2)若H为PC的中点,
,PA与平面ABCD所成的角为60°,求AD与平面AMHN所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb86d420c825e9dbb9686784f6d4eb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f306ff6d237cd9d847aa109acf9333d7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/25/7e759ab8-6677-4d09-8c63-b963dc0752cc.png?resizew=237)
(1)证明;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11af43b6fbbd2d71f0a30f4a84ce9093.png)
(2)若H为PC的中点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83c2fb70ff4c51c80bd6013d8006a17.png)
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2022-10-23更新
|
835次组卷
|
5卷引用:吉林省长春市长春吉大附中实验学校2022-2023学年高二上学期10月月考数学试题
名校
解题方法
2 . 如图.在三棱柱
中,四边形
是边长为
的正方形,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/25/8955a837-6e73-4d18-9cca-4bf5e2bb496f.png?resizew=159)
(1)证明:平面
平面
;
(2)若点M在线段
上且满足
.求直线CM与
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cf3bff56a7f4ab6c0008e90823025d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445cfd832967db6bbaa0a2ea311b4f0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef812f839622326a7d7027cc806aaeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/551ca28888bdc921c659b9bb8eae1424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e0b10b0e45ee1193ab26836bf1ff0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93edbd735d79524f463085a4e9093bd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/25/8955a837-6e73-4d18-9cca-4bf5e2bb496f.png?resizew=159)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f841e3f3fd5a2380ff990557fe50570a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d63354d35b9eef8732c993abe89f25e.png)
(2)若点M在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9756b7c2a9f0cb5a1b025ad4821abdcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915f72b23e6d066784713909386d221f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f73038249a611568193c0bcc286fd7.png)
您最近一年使用:0次
2022-10-23更新
|
344次组卷
|
3卷引用:吉林省长春市长春吉大附中实验学校2022-2023学年高二上学期10月月考数学试题
吉林省长春市长春吉大附中实验学校2022-2023学年高二上学期10月月考数学试题福建省南安市柳城中学2022-2023学年高二上学期11月期中考试数学试题(已下线)湖南省长沙市长郡中学2024届高三上学期月考(二)数学试题变式题19-22
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3 . 在三棱锥
中,
,点
在平面
中的射影是
的垂心,若
,
,
的面积之和为4,则三棱锥
的外接球表面积的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
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2022-09-29更新
|
570次组卷
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5卷引用:吉林省东北师范大学附属中学2022-2023学年高二上学期第一次月考数学试题
吉林省东北师范大学附属中学2022-2023学年高二上学期第一次月考数学试题(已下线)考向30 立体几何中的最值、翻折、探索性问题(重点)浙江省学军中学紫金港2022-2023学年高二上学期期中数学试题(已下线)第32讲直线与平面垂直2(已下线)专题训练:与球有关的外接和相切问题-【题型分类归纳】
名校
4 . 如图,在直三棱柱
中,
,
,
分别为
和
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/2/784ab481-ce59-43f1-8506-17c6dc6c21a5.png?resizew=151)
(1)求证:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d355b4c58b4e883b9e65cc6da8622e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0023280949eda97787964f0a9d41ed2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/2/784ab481-ce59-43f1-8506-17c6dc6c21a5.png?resizew=151)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0451505215f3b34ca3bacf948251f70.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
您最近一年使用:0次
2022-09-29更新
|
434次组卷
|
2卷引用:吉林省东北师范大学附属中学2022-2023学年高二上学期第一次月考数学试题
名校
解题方法
5 . 如图,在边长为2的正方体
中,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/543dba1f-4a3a-4442-9648-7a8a1a1a4028.png?resizew=145)
(1)证明:
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d572fdea0ba4336ccf77c76db7f0332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e5ee662272a9cda713dcff67f57155.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/543dba1f-4a3a-4442-9648-7a8a1a1a4028.png?resizew=145)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae15ccbbb50c42c05ad50bcfa63e85dd.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
您最近一年使用:0次
2022-09-28更新
|
1660次组卷
|
7卷引用:吉林省长春外国语学校2022-2023学年高二上学期第一次月考数学试题
名校
解题方法
6 . 如图,等边三角形ABC的中线AF与中位线DE相交于G,已知
是
绕DE旋转过程中的一个图形,下列命题中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/31/8872722a-5dc9-4604-ab1f-9be817811caa.png?resizew=207)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a49088d8f4cae827c70a903191f7a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/31/8872722a-5dc9-4604-ab1f-9be817811caa.png?resizew=207)
A.动点![]() |
B.恒有![]() ![]() |
C.三棱锥![]() |
D.异面直线![]() |
您最近一年使用:0次
7 . 已知平面
,
和直线m,给出条件:①
;②
;③
;④
.当满足条件______ 时,有
.(选填其中的两个条件)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58645e141cf81e1962ec8692e5edbfa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe920cd78db25f5b4df37d066e57800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/539a38ada26356d73024fb8533449c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b303b1f07604f5303aea94df7f0518e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b610e3c5b3d78a5730e7f3d736ac28.png)
您最近一年使用:0次
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解题方法
8 . 如果直线l,m与平面
,
,
满足:
,
,
和
,那么必有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74201830e454225893a1a33f242f53bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad25ad7785af488a004cae4436019ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/539a38ada26356d73024fb8533449c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008241f4c7f47526109c74c92ed21fdb.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 如图,已知圆柱
,过轴
的截面图形
为正方形,点
在底面圆周上,且
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/2/24415e6a-5152-4368-b6e3-44fba78012f8.png?resizew=188)
(1)求证:
平面
;
(2)求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/837510568cd16b70c4e038ccaf0feb3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/2/24415e6a-5152-4368-b6e3-44fba78012f8.png?resizew=188)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2730b513bd3359c3dfe6567e04f5ef9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53bdef2e7a7929ad6190302ab44c46c0.png)
您最近一年使用:0次
2022-08-30更新
|
690次组卷
|
4卷引用:吉林省东北师范大学附属中学2022-2023学年高二上学期大练习一数学试题
吉林省东北师范大学附属中学2022-2023学年高二上学期大练习一数学试题河南省商城县观庙高级中学2022-2023学年高二上学期第一次月考理科数学试题山西省山西大学附属中学校2022-2023学年高二上学期10月(第二次模块诊断测试)数学试题(已下线)高二数学上学期【第一次月考卷】(测试范围:第1~2章)-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)
10 . 如图,四棱锥
中,
平面
,底面
是正方形,
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/27/d698b7c4-82df-4b3e-8be3-da7248d33cc8.png?resizew=178)
(1)求证:
平面
;
(2)求平面
和平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99926bf272cd757f0985c69b390ebcce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/27/d698b7c4-82df-4b3e-8be3-da7248d33cc8.png?resizew=178)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次